Texture mapping single 3D object with one draw call

Hi!
I cannot seem to be able to texture map from one spritesheet with different iamges for different sides of a cube with one draw call.
I can accomplish this using 6 glDrawArrays call for each side and binding different parts of the spritesheet with each call.

Ought to be simple. Use GL_QUADS or GL_TRIANGLES (not one of the types like GL_TRIANGLE_STRIP that shares vertices between primitives), and pass different texture coordinates in your texCoord array for each face you draw.